Axe is way easier to make, yes, but Axe Grids are not great. What you gain is a good chunk of base Atk, while you lose one weapon slot Assault. The net result of this is roughly +-0 damage gain.
So, non-Assault Phantom weapons Grids effectively only gain the two skills from the Phantom weapon - and in the case of the Axe, that's Ability(++) and Exceed(++). The gain of which is... not... particularly impressive. As such, is using a Phantom Axe Grid an upgrade? Yes, yes it is. Is it worth investing your resources in? ... well, no. Not really.
As such, you should always aim for Lance/Hammer/Glaive/Bow Phantom Grids, if possible (and this is obviously hard). That way, you gain the chunk of base Atk without losing the Assault. This is a very nice DPS boost.